MATH117 Lecture Notes - Lecture 6: Partial Fraction Decomposition, Synthetic Division, Asymptote

• School: University of Waterloo
• Department: Mathematics
• Course: MATH117
• Professor: David Harmsworth

Document Summary

A rational function is a ratio of polynomials, such as x2 4x + 1 x3 + 5x2 3. We call a rational function proper if the degree of the numerator is less than the degree of the denominator, and improper otherwise1. You should be quite comfortable with the idea of combining rational functions into one through nding a common denominator, but in calculus we will often nd it necessary to reverse this procedure. Fortunately, this can always be done provided that we can manage to factor the denominator. Fact: any proper rational function can be expressed as the sum of simpler rational functions, whose denominators are either linear or irreducibly quadratic. 3x 1 x2 + x + 1. The method of partial fractions essentially consists of guessing the form of the decomposition on the right by taking advantage of the experience we have in working in the other direction.